Specifications

University of Pretoria etd – Combrinck, M (2006)
system data and only results applied to synthetic data are available in literature (GEOTEM
is a registered trademark of Geoterrex).
DEPTH (h)
(
A
PP
A
RENT) C
O
NDUCTIVITY
10
0
10
1
10
2
10
3
10
0
10
1
10
2
10
-1
10
-2
DEPTH (h)
10
0
10
1
10
2
10
0
10
1
10
2
10
-1
10
-2
DEPTH (h)
10
0
10
1
10
2
10
3
10
0
10
1
10
2
10
-1
10
-2
DEPTH (h)
(APPARENT) CONDUCTIVITY
10
0
10
1
10
2
10
0
10
1
10
2
Figure 3-1 Comparison of apparent conductivity (calculated by differentiating the fitted
slowness with respect to reference depth curve) with the actual conductivity for four three-layer
models (after Macnae and Lamontagne, 1987).
3.6.3 S-layer differential transform
The S-layer differential transform was originally developed by Sidorov and Tikshaev (1969)
and extended to an inversion technique by Tartaras et al., (2000). It is based on the late-
time ∂B
z
/∂t approximation of the S-layer model. The derivative of this equation (∂
2
B
z
/∂t
2
)
is calculated and from these two equations the variables S (cumulative conductance) and d
(depth) can be solved for at every time channel. Taking the partial derivative of S to d
(∂S/∂d) gives the conductivity of a thin layer at depth d. The actual calculations are
remarkably simple and when working in a conductive, layered region this method gives
good results. The main criticism against the method (Tartaras et al., 2000) is the fact that it
contains two numerical differentiations which are numerically unstable operators and
therefore is extremely sensitive to noise. It is further based on the one-dimensional and
late-time assumptions. Although, for the central-loop sounding geometry it can be shown
(Tartaras et. al., 2000) that measured data almost always satisfy the late-time prerequisite.
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